Show that the Pythagorean identity sin^2 θ+cos^2 θ=1 is true for the given angle. θ= 5π/3

Pythagorean identity sin²θ+cos²θ = 1 is true for the angle θ =

Step-by-step explanation:

At first, let us simplify the left side of the identity

∵ The left side is sin²Ф + cos²Ф

∵ Ф = ⇒ lies in the 4th quadrant

∴ The left side is sin²() + cos²()

→ Let us write the values of sin() and cos()

∵ sin() = ⇒ sine an angle in the 4th quadrant is -ve

∵ cos() = ⇒ cosine an angle in the 4th quadrant is +ve

→ Substitute them in the left side

∵ sin²() + cos²() = [ ]² + []²

∴ sin²() + cos²() = [] + []

∴ sin²() + cos²() = []

∴ sin²() + cos²() = 1

∵ The right side = 1

∴ Left side = Right side

∴ sin²() + cos²() = 1 ⇒ proved

∴ Pythagorean identity sin²θ+cos²θ = 1 is true for the angle θ =

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step-by-step explanation:

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